Least Common Multiple (LCM) of 196 and 110
The least common multiple (LCM) of 196 and 110 is 10780.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 196 and 110?
First, calculate the GCD of 196 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 110 = 1 remainder 86 |
| 2 | 110 ÷ 86 = 1 remainder 24 |
| 3 | 86 ÷ 24 = 3 remainder 14 |
| 4 | 24 ÷ 14 = 1 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 98 | 3038 |
| 72 and 133 | 9576 |
| 12 and 141 | 564 |
| 60 and 170 | 1020 |
| 15 and 44 | 660 |